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Finite-time blow-up of the heat flow of harmonic maps from surfaces. (English) Zbl 0765.53026

This paper is concerned with the singular behaviour of solutions to the heat equation of harmonic maps between Riemannian manifolds. The authors construct examples of finite-time blow-up of the solutions in the case where the domain manifold has dimension two for the first time.

MSC:

53C20 Global Riemannian geometry, including pinching
58E20 Harmonic maps, etc.
58J35 Heat and other parabolic equation methods for PDEs on manifolds
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